In this paper we show that if $n\geq 5$ and $G$ is any of the groups $SU_n(q)$ with $n\neq 6,$ $Sp_{2n}(q)$ with $q$ odd, $\Omega_{2n+1}(q),$ $\Omega_{2n}^{\pm}(q),$ then $G$ and the simple group $\overline G=G/Z(G)$ are not 2-coverable. Moreover the only 2-covering of $Sp_{2n}(q),$ with $q$ even, has components $ O^-_{2n}(q)$ and $O^{+}_{2n}(q) .$
2-Coverings of classical groups / D. Bubboloni; M.S. Lucido; T. Weigel. - ELETTRONICO. - arxiv: 1102.0660v1:(2011), pp. 1-19.
2-Coverings of classical groups
BUBBOLONI, DANIELA;
2011
Abstract
In this paper we show that if $n\geq 5$ and $G$ is any of the groups $SU_n(q)$ with $n\neq 6,$ $Sp_{2n}(q)$ with $q$ odd, $\Omega_{2n+1}(q),$ $\Omega_{2n}^{\pm}(q),$ then $G$ and the simple group $\overline G=G/Z(G)$ are not 2-coverable. Moreover the only 2-covering of $Sp_{2n}(q),$ with $q$ even, has components $ O^-_{2n}(q)$ and $O^{+}_{2n}(q) .$
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